Junior in an Interesting Situation

[mariogs379]

Hey guys,

I'm a junior at an ivy in an interesting situation. I did math at the start of college but switched midway through to philosophy. I haven't done math during my junior year but want to get back into it.

Here's my background:

Calc 2 (A), Multivariable Calc (A), ODE's (A), Linear Algebra (B+)

I have a few questions:

1) What should I take during my senior year to see if I want to do higher level math and prepare for the possibility of grad school? I was thinking real analysis and probability theory in the fall, and statistics and algebra in the spring...

2) Supposing I like the courses I take during senior year, how should I go about taking more math? It seems like I won't be a competitive Ph.D. candidate and that an MA program is a better choice (a bit less competitive, can transition to Ph.D. if I want, not committed to Ph.D.) Any ideas here?

Thanks for your help,

Mariogs

[origin415]

Your professors would be the best people to talk to, they would know more about your individual situation, what graduate schools want, and what your school has to offer to get you there.

Regardless, algebra and analysis are essential, if at all possible topology too. You are going to want more than those 4 courses you listed definitely. Depending on what mathematics you are interested in probablity and statistics could be useless or essential.

[Slarti]

Definately take Algebra and Analysis, and as many other upper level (proof based) courses as you are comfortable with. Probability Theory sounds like a good idea, but I'm not too sure about Statistics since it is often taught at a lower level and is not always proof based.

I'd suggest applying to both Ph.D. and MA programs, but talk to your advisor as they'll be more able to assess your chances of getting in.

[Kathryn]

Definitely abstract algebra and real analysis. If you're doing stats, make sure it's calc based stats.

I would probably look more into other proof based courses like a basic proof course or a number theory course. The more experience you have, the better off you'll be.

Maybe try for a PDE course or complex analysis.

I guess as far as master's vs PhD, if you don't feel confident enough for a PhD at this time try for a master's and take that time to get your feel for graduate level work and what areas really interest you.

[BongRips69]

Algebra and analysis, as others have said.

You could probably teach yourself enough statistics (and even the calc-based stuff) to cover the subject GRE... so I wouldn't worry about those classes unless you'd like to go into that field. Instead, take more algebra and analysis or maybe topology, complex analysis, combinatorics or number theory.... again, depending on your interests.

Can you take classes this summer?

Edited March 20, 2010 by BongRips69

[mariogs379]

Algebra and analysis, as others have said.

You could probably teach yourself enough statistics (and even the calc-based stuff) to cover the subject GRE... so I wouldn't worry about those classes unless you'd like to go into that field. Instead, take more algebra and analysis or maybe topology, complex analysis, combinatorics or number theory.... again, depending on your interests.

Can you take classes this summer?

Hey guys,

Thanks for the responses. I'm still trying to figure out coursework. I'm going abroad in the fall to University College London and can have my pick of classes there. Complex analysis is not offered in the spring at my school, but real analysis, algebra, and number theory all are. It seems like it would make sense to take probability and algebra 2 at UCL (here's the link: http://www.ucl.ac.uk...ses/index.html) and then real analysis in the spring. Number theory assumes abstract algebra and it's not clear to me that algebra 2 covers rings and fields (which you need for number theory at my school)...My school also uses herstein for algebra, so that's pretty rough going...

Any more advice would be awesome (and probability requires multivariable calc)

Mariogs

P.S. Can't take summer classes; doing an internship

Edited March 25, 2010 by mariogs379

[someDay]

mariogs379,

I would imagine UCL stipulates that you take at the very least Honours Y2 modules; and possibley even requires to you take some Y3 ones. If you think you can do a PhD, then you really *should* take a lot of Y3 ones and put a tremendous amount of work and effort in, but you'd not see much of London.

I suggest you delay choosing your modules until you're in London and had a talk with your tutor about this.

sD.

[mariogs379]

Hey there,

Well I'm not a math major and I got into UCL's philosophy dept. Having said that, I can take up to 2 non-phil classes so I'll do that. Thoughts on which they should be? I'm sort of resigned to the fact that I won't be a competitive applicant until after I graduate from college...yeah?

Also, any thoughts on the benefits of applying to masters programs vs. phd ones? Seems like phd is better because I wouldn't have to pay, some offer terminal master's if you wanna leave, and...eh?

Thanks

[origin415]

Its looking like you might want to apply to some masters programs in addition to applying to phd programs at the very least. Well, as long as you are willing to pay. There are also departments with both phd and masters programs, and will automatically consider you for the masters if you aren't prepared for the phd. Off hand, I know Washington and UIC does this, but I haven't been researching this, so you might look into that, which will allow you to cover your bases. NYU offering masters without funding to their PhD applicants is basically their version of rejection, too. Overall though, not many american universities offer strong masters programs, so you can also look abroad.

No matter what you do, its very important you take the math gre this fall and kick ass at it. Buy some books and study over the summer. I don't know how it works with taking it abroad though.

[someDay]

I respectfully disagree with origin415 here - given your background, it would appear extremely difficult to get into a decent PhD programme, solely because you've not seen much - if any - serious mathematics. You might rise to the challenge, but adcoms at decent schools won't take that much of a gamble. You should take modules in algebra and analysis (forget about number theory, stats, calc or anything applied ) to survive the first year of a master's degree. I strongly advise you to not look abroad for master's degree, as a master's degree in most non-US countries is a preparation for a 3 years PhD and therefore require a roughly similar background for admission to master's degrees as US unis do for admissions to PhD.

sD.

[mariogs379]

I respectfully disagree with origin415 here - given your background, it would appear extremely difficult to get into a decent PhD programme, solely because you've not seen much - if any - serious mathematics. You might rise to the challenge, but adcoms at decent schools won't take that much of a gamble. You should take modules in algebra and analysis (forget about number theory, stats, calc or anything applied ) to survive the first year of a master's degree. I strongly advise you to not look abroad for master's degree, as a master's degree in most non-US countries is a preparation for a 3 years PhD and therefore require a roughly similar background for admission to master's degrees as US unis do for admissions to PhD.

sD.

Thanks for the responses,

@sD,

Can you take a look on UCL's website (the link I provided)? It's not clear that algebra 2 at UCL is going to give me good enough background in algebra. I've taken a proof-based course on linear algebra in the US, so I'm a bit lost on the algebra front is all. I think I'm really going to like probability so I want to take that. I'll take analysis in the spring and then maybe abstract algebra (given that the algebra class at UCL might be more like a second course in linear algebra...)

What do you think?

Also, after I graduate, how competitive do you think my profile will be:

multivariable

ODEs

linear algebra

probability

algebra 2 (2nd course in linear it seems like)

analysis

Thanks so much,

Mariogs

[someDay]

I don't know much about US Masters, but if you applied to UK unis (for an MS), they'd probably accept you into their Bachelor's programme and let you skip the first year. If you're serious about a maths PhD, then I would recommend Algebra 4 or even Commutative Algebra, but it just might not be worth missing out on social life in London. (Which is awesome.)

sD.

[mariogs379]

They might accept me for their bachelor's and let me skip the first year? So would I be doing an MS or another B.A.?

It seems like, if you've done linear algebra (proof-based) in the US...algebra 2 is the next one in line, yeah?

[someDay]

They might accept me for their bachelor's and let me skip the first year? So would I be doing an MS or another B.A.?

Another BA.

I don't really know what you mean by proof-based linear algebra. Algebra 2 will essentially introduce you to the concept of a group and some first theorems in linear algebra. Bear in mind this is a course for first year students (first year = party, as it doesn't count towards your degree), so essentially it's some boring crap for lazy people suffering from hangover. If you're serious I'd advise you to take Algebra 4 instead, which is still fairly elementary, so you wouldn't be completely lost.

sD.